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Chords of magic

Edit 0 5 …
Below are listed the dyadic chords of 11-limit magic temperament. Typing the chords requires consideration of the fact that magic conflates 10/9 and 11/10 and so also 9/5 and 20/11. If a transversal can be found which shows the chord to be essentially just, that transversal is listed along with a typing as otonal, utonal, or ambitonal. If the chord is essentially tempered, it is analyzed in terms of the transversal which employs 10/9 and 9/5.

Chords requiring tempering only by 225/224 are labeled marvel, by 245/243 sensamagic, by 100/99 ptolemismic, by 896/891 pentacircle, by 385/384 keenanismic, and by 540/539 swetismic. Those requiring any two of 225/225, 100/99 or 896/891 are labeled apollo, any two of 100/99, 245/243 or 540/539 octarod, any two of 245/243, 896/891 or 385/384 sensamagic11, any two of 225/224, 385/384 or 540/539 unimarvel. Chords requiring both 100/99 and 385/384 are labeled supermagic. Finally, anything requiring three independent commas among those discussed above is labeled magic.

Magic has MOS of sizes 7, 10, 13, 16, 19 and 22 notes. It may be seen that even the seven note MOS is not without a few harmonic resources, and the larger MOS do much better.

Triads

Number
 Chord
 Transversal
 Type
1
 0-1-2
 1-5/4-14/9
 marvel
2
 0-2-4
 1-14/9-6/5
 sensamagic
3
 0-1-5
 1-5/4-3/2
 otonal
4
 0-4-5
 1-6/5-3/2
 utonal
5
 0-2-7
 1-14/9-7/6
 utonal
6
 0-5-7
 1-3/2-7/6
 otonal
7
 0-1-8
 1-5/4-16/11
 keenanismic
8
 0-4-8
 1-6/5-16/11
 ptolemismic
9
 0-7-8
 1-7/6-16/11
 keenanismic
10
 0-1-9
 1-5/4-20/11
 utonal
11
 0-2-9
 1-14/9-9/5
 sensamagic
12
 0-4-9
 1-6/5-9/5
 otonal
13
 0-5-9
 1-3/2-9/5
 utonal
14
 0-7-9
 1-7/6-9/5
 sensamagic
15
 0-8-9
 1-16/11-20/11
 otonal
16
 0-1-10
 1-5/4-9/8
 otonal
17
 0-2-10
 1-14/9-9/8
 pentacircle
18
 0-5-10
 1-3/2-9/8
 ambitonal
19
 0-8-10
 1-16/11-9/8
 pentacircle
20
 0-9-10
 1-9/5-9/8
 utonal
21
 0-1-11
 1-5/4-7/5
 marvel
22
 0-2-11
 1-14/9-7/5
 utonal
23
 0-4-11
 1-6/5-7/5
 otonal
24
 0-7-11
 1-7/6-7/5
 utonal
25
 0-9-11
 1-9/5-7/5
 otonal
26
 0-10-11
 1-9/8-7/5
 marvel
27
 0-1-12
 1-5/4-7/4
 otonal
28
 0-2-12
 1-14/9-7/4
 utonal
29
 0-4-12
 1-6/5-7/4
 keenanismic
30
 0-5-12
 1-3/2-7/4
 otonal
31
 0-7-12
 1-7/6-7/4
 utonal
32
 0-8-12
 1-16/11-7/4
 keenanismic
33
 0-10-12
 1-9/8-7/4
 otonal
34
 0-11-12
 1-7/5-7/4
 utonal
35
 0-1-13
 1-5/4-12/11
 keenanismic
36
 0-2-13
 1-14/9-12/11
 swetismic
37
 0-4-13
 1-6/5-12/11
 utonal
38
 0-5-13
 1-3/2-12/11
 utonal
39
 0-8-13
 1-16/11-12/11
 otonal
40
 0-9-13
 1-20/11-12/11
 otonal
41
 0-11-13
 1-7/5-12/11
 swetismic
42
 0-12-13
 1-7/4-12/11
 keenanismic
43
 0-5-18
 1-3/2-18/11
 utonal
44
 0-7-18
 1-7/6-18/11
 swetismic
45
 0-8-18
 1-16/11-18/11
 otonal
46
 0-9-18
 1-9/5-18/11
 utonal
47
 0-10-18
 1-9/8-18/11
 utonal
48
 0-11-18
 1-7/5-18/11
 swetismic
49
 0-13-18
 1-12/11-18/11
 otonal
50
 0-2-20
 1-14/9-14/11
 utonal
51
 0-7-20
 1-7/6-14/11
 utonal
52
 0-8-20
 1-16/11-14/11
 otonal
53
 0-9-20
 1-20/11-14/11
 otonal
54
 0-10-20
 1-9/8-14/11
 pentacircle
55
 0-11-20
 1-7/5-14/11
 utonal
56
 0-12-20
 1-7/4-14/11
 utonal
57
 0-13-20
 1-12/11-14/11
 otonal
58
 0-18-20
 1-18/11-14/11
 otonal

Tetrads

Number
 Chord
 Transversal
 Type
1
 0-1-2-9
 1-5/4-14/9-9/5
 magic
2
 0-2-4-9
 1-14/9-6/5-9/5
 sensamagic
3
 0-1-5-9
 1-5/4-3/2-9/5
 ptolemismic
4
 0-4-5-9
 1-6/5-3/2-9/5
 ambitonal
5
 0-2-7-9
 1-14/9-7/6-9/5
 sensamagic
6
 0-5-7-9
 1-3/2-7/6-9/5
 sensamagic
7
 0-1-8-9
 1-5/4-16/11-9/5
 supermagic
8
 0-4-8-9
 1-6/5-16/11-9/5
 ptolemismic
9
 0-7-8-9
 1-7/6-16/11-9/5
 magic
10
 0-1-2-10
 1-5/4-14/9-9/8
 apollo
11
 0-1-5-10
 1-5/4-3/2-9/8
 otonal
12
 0-1-8-10
 1-5/4-16/11-9/8
 sensamagic11
13
 0-1-9-10
 1-5/4-9/5-9/8
 ptolemismic
14
 0-2-9-10
 1-14/9-9/5-9/8
 sensamagic11
15
 0-5-9-10
 1-3/2-9/5-9/8
 utonal
16
 0-8-9-10
 1-16/11-9/5-9/8
 apollo
17
 0-1-2-11
 1-5/4-14/9-7/5
 marvel
18
 0-2-4-11
 1-14/9-6/5-7/5
 sensamagic
19
 0-2-7-11
 1-14/9-7/6-7/5
 utonal
20
 0-1-9-11
 1-5/4-9/5-7/5
 apollo
21
 0-2-9-11
 1-14/9-9/5-7/5
 sensamagic
22
 0-4-9-11
 1-6/5-9/5-7/5
 otonal
23
 0-7-9-11
 1-7/6-9/5-7/5
 sensamagic
24
 0-1-10-11
 1-5/4-9/8-7/5
 marvel
25
 0-2-10-11
 1-14/9-9/8-7/5
 apollo
26
 0-9-10-11
 1-9/5-9/8-7/5
 marvel
27
 0-1-2-12
 1-5/4-14/9-7/4
 marvel
28
 0-2-4-12
 1-14/9-6/5-7/4
 sensamagic11
29
 0-1-5-12
 1-5/4-3/2-7/4
 otonal
30
 0-4-5-12
 1-6/5-3/2-7/4
 keenanismic
31
 0-2-7-12
 1-14/9-7/6-7/4
 utonal
32
 0-5-7-12
 1-3/2-7/6-7/4
 ambitonal
33
 0-1-8-12
 1-5/4-16/11-7/4
 keenanismic
34
 0-4-8-12
 1-6/5-16/11-7/4
 supermagic
35
 0-7-8-12
 1-7/6-16/11-7/4
 keenanismic
36
 0-1-10-12
 1-5/4-9/8-7/4
 otonal
37
 0-2-10-12
 1-14/9-9/8-7/4
 pentacircle
38
 0-5-10-12
 1-3/2-9/8-7/4
 otonal
39
 0-8-10-12
 1-16/11-9/8-7/4
 sensamagic11
40
 0-1-11-12
 1-5/4-7/5-7/4
 marvel
41
 0-2-11-12
 1-14/9-7/5-7/4
 utonal
42
 0-4-11-12
 1-6/5-7/5-7/4
 keenanismic
43
 0-7-11-12
 1-7/6-7/5-7/4
 utonal
44
 0-10-11-12
 1-9/8-7/5-7/4
 marvel
45
 0-1-2-13
 1-5/4-14/9-12/11
 unimarvel
46
 0-2-4-13
 1-14/9-6/5-12/11
 octarod
47
 0-1-5-13
 1-5/4-3/2-12/11
 keenanismic
48
 0-4-5-13
 1-6/5-3/2-12/11
 utonal
49
 0-1-8-13
 1-5/4-16/11-12/11
 keenanismic
50
 0-4-8-13
 1-6/5-16/11-12/11
 ptolemismic
51
 0-1-9-13
 1-5/4-9/5-12/11
 supermagic
52
 0-2-9-13
 1-14/9-9/5-12/11
 octarod
53
 0-4-9-13
 1-6/5-9/5-12/11
 ptolemismic
54
 0-5-9-13
 1-3/2-9/5-12/11
 ptolemismic
55
 0-8-9-13
 1-16/11-20/11-12/11
 otonal
56
 0-1-11-13
 1-5/4-7/5-12/11
 unimarvel
57
 0-2-11-13
 1-14/9-7/5-12/11
 swetismic
58
 0-4-11-13
 1-6/5-7/5-12/11
 octarod
59
 0-9-11-13
 1-9/5-7/5-12/11
 octarod
60
 0-1-12-13
 1-5/4-7/4-12/11
 keenanismic
61
 0-2-12-13
 1-14/9-7/4-12/11
 unimarvel
62
 0-4-12-13
 1-6/5-7/4-12/11
 supermagic
63
 0-5-12-13
 1-3/2-7/4-12/11
 keenanismic
64
 0-8-12-13
 1-16/11-7/4-12/11
 keenanismic
65
 0-11-12-13
 1-7/5-7/4-12/11
 unimarvel
66
 0-5-7-18
 1-3/2-7/6-18/11
 swetismic
67
 0-7-8-18
 1-7/6-16/11-18/11
 unimarvel
68
 0-5-9-18
 1-3/2-9/5-18/11
 utonal
69
 0-7-9-18
 1-7/6-9/5-18/11
 octarod
70
 0-8-9-18
 1-16/11-20/11-18/11
 otonal
71
 0-5-10-18
 1-3/2-9/8-18/11
 utonal
72
 0-8-10-18
 1-16/11-9/8-18/11
 pentacircle
73
 0-9-10-18
 1-9/5-9/8-18/11
 utonal
74
 0-7-11-18
 1-7/6-7/5-18/11
 swetismic
75
 0-9-11-18
 1-9/5-7/5-18/11
 octarod
76
 0-10-11-18
 1-9/8-7/5-18/11
 unimarvel
77
 0-5-13-18
 1-3/2-12/11-18/11
 ambitonal
78
 0-8-13-18
 1-16/11-12/11-18/11
 otonal
79
 0-9-13-18
 1-20/11-12/11-18/11
 otonal
80
 0-11-13-18
 1-7/5-12/11-18/11
 swetismic
81
 0-2-7-20
 1-14/9-7/6-14/11
 utonal
82
 0-7-8-20
 1-7/6-16/11-14/11
 keenanismic
83
 0-2-9-20
 1-14/9-9/5-14/11
 octarod
84
 0-7-9-20
 1-7/6-9/5-14/11
 octarod
85
 0-8-9-20
 1-16/11-20/11-14/11
 otonal
86
 0-2-10-20
 1-14/9-9/8-14/11
 pentacircle
87
 0-8-10-20
 1-16/11-9/8-14/11
 pentacircle
88
 0-9-10-20
 1-9/5-9/8-14/11
 apollo
89
 0-2-11-20
 1-14/9-7/5-14/11
 utonal
90
 0-7-11-20
 1-7/6-7/5-14/11
 utonal
91
 0-9-11-20
 1-9/5-7/5-14/11
 ptolemismic
92
 0-10-11-20
 1-9/8-7/5-14/11
 apollo
93
 0-2-12-20
 1-14/9-7/4-14/11
 utonal
94
 0-7-12-20
 1-7/6-7/4-14/11
 utonal
95
 0-8-12-20
 1-16/11-7/4-14/11
 keenanismic
96
 0-10-12-20
 1-9/8-7/4-14/11
 pentacircle
97
 0-11-12-20
 1-7/5-7/4-14/11
 utonal
98
 0-2-13-20
 1-14/9-12/11-14/11
 swetismic
99
 0-8-13-20
 1-16/11-12/11-14/11
 otonal
100
 0-9-13-20
 1-20/11-12/11-14/11
 otonal
101
 0-11-13-20
 1-7/5-12/11-14/11
 octarod
102
 0-12-13-20
 1-7/4-12/11-14/11
 keenanismic
103
 0-7-18-20
 1-7/6-18/11-14/11
 swetismic
104
 0-8-18-20
 1-16/11-18/11-14/11
 otonal
105
 0-9-18-20
 1-20/11-18/11-14/11
 otonal
106
 0-10-18-20
 1-9/8-18/11-14/11
 pentacircle
107
 0-11-18-20
 1-7/5-18/11-14/11
 octarod
108
 0-13-18-20
 1-12/11-18/11-14/11
 otonal

Pentads

Number
 Chord
 Transversal
 Type
1
 0-1-2-9-10
 1-5/4-14/9-9/5-9/8
 magic
2
 0-1-5-9-10
 1-5/4-3/2-9/5-9/8
 ptolemismic
3
 0-1-8-9-10
 1-5/4-16/11-9/5-9/8
 magic
4
 0-1-2-9-11
 1-5/4-14/9-9/5-7/5
 magic
5
 0-2-4-9-11
 1-14/9-6/5-9/5-7/5
 sensamagic
6
 0-2-7-9-11
 1-14/9-7/6-9/5-7/5
 sensamagic
7
 0-1-2-10-11
 1-5/4-14/9-9/8-7/5
 apollo
8
 0-1-9-10-11
 1-5/4-9/5-9/8-7/5
 apollo
9
 0-2-9-10-11
 1-14/9-9/5-9/8-7/5
 magic
10
 0-1-2-10-12
 1-5/4-14/9-9/8-7/4
 apollo
11
 0-1-5-10-12
 1-5/4-3/2-9/8-7/4
 otonal
12
 0-1-8-10-12
 1-5/4-16/11-9/8-7/4
 sensamagic11
13
 0-1-2-11-12
 1-5/4-14/9-7/5-7/4
 marvel
14
 0-2-4-11-12
 1-14/9-6/5-7/5-7/4
 sensamagic11
15
 0-2-7-11-12
 1-14/9-7/6-7/5-7/4
 utonal
16
 0-1-10-11-12
 1-5/4-9/8-7/5-7/4
 marvel
17
 0-2-10-11-12
 1-14/9-9/8-7/5-7/4
 apollo
18
 0-1-2-9-13
 1-5/4-14/9-9/5-12/11
 magic
19
 0-2-4-9-13
 1-14/9-6/5-9/5-12/11
 octarod
20
 0-1-5-9-13
 1-5/4-3/2-9/5-12/11
 supermagic
21
 0-4-5-9-13
 1-6/5-3/2-9/5-12/11
 ptolemismic
22
 0-1-8-9-13
 1-5/4-16/11-9/5-12/11
 supermagic
23
 0-4-8-9-13
 1-6/5-16/11-9/5-12/11
 ptolemismic
24
 0-1-2-11-13
 1-5/4-14/9-7/5-12/11
 unimarvel
25
 0-2-4-11-13
 1-14/9-6/5-7/5-12/11
 octarod
26
 0-1-9-11-13
 1-5/4-9/5-7/5-12/11
 magic
27
 0-2-9-11-13
 1-14/9-9/5-7/5-12/11
 octarod
28
 0-4-9-11-13
 1-6/5-9/5-7/5-12/11
 octarod
29
 0-1-2-12-13
 1-5/4-14/9-7/4-12/11
 unimarvel
30
 0-2-4-12-13
 1-14/9-6/5-7/4-12/11
 magic
31
 0-1-5-12-13
 1-5/4-3/2-7/4-12/11
 keenanismic
32
 0-4-5-12-13
 1-6/5-3/2-7/4-12/11
 supermagic
33
 0-1-8-12-13
 1-5/4-16/11-7/4-12/11
 keenanismic
34
 0-4-8-12-13
 1-6/5-16/11-7/4-12/11
 supermagic
35
 0-1-11-12-13
 1-5/4-7/5-7/4-12/11
 unimarvel
36
 0-2-11-12-13
 1-14/9-7/5-7/4-12/11
 unimarvel
37
 0-4-11-12-13
 1-6/5-7/5-7/4-12/11
 magic
38
 0-5-7-9-18
 1-3/2-7/6-9/5-18/11
 octarod
39
 0-7-8-9-18
 1-7/6-16/11-9/5-18/11
 magic
40
 0-5-9-10-18
 1-3/2-9/5-9/8-18/11
 utonal
41
 0-8-9-10-18
 1-16/11-9/5-9/8-18/11
 apollo
42
 0-7-9-11-18
 1-7/6-9/5-7/5-18/11
 octarod
43
 0-9-10-11-18
 1-9/5-9/8-7/5-18/11
 magic
44
 0-5-9-13-18
 1-3/2-9/5-12/11-18/11
 ptolemismic
45
 0-8-9-13-18
 1-16/11-20/11-12/11-18/11
 otonal
46
 0-9-11-13-18
 1-9/5-7/5-12/11-18/11
 octarod
47
 0-2-7-9-20
 1-14/9-7/6-9/5-14/11
 octarod
48
 0-7-8-9-20
 1-7/6-16/11-9/5-14/11
 magic
49
 0-2-9-10-20
 1-14/9-9/5-9/8-14/11
 magic
50
 0-8-9-10-20
 1-16/11-9/5-9/8-14/11
 apollo
51
 0-2-7-11-20
 1-14/9-7/6-7/5-14/11
 utonal
52
 0-2-9-11-20
 1-14/9-9/5-7/5-14/11
 octarod
53
 0-7-9-11-20
 1-7/6-9/5-7/5-14/11
 octarod
54
 0-2-10-11-20
 1-14/9-9/8-7/5-14/11
 apollo
55
 0-9-10-11-20
 1-9/5-9/8-7/5-14/11
 apollo
56
 0-2-7-12-20
 1-14/9-7/6-7/4-14/11
 utonal
57
 0-7-8-12-20
 1-7/6-16/11-7/4-14/11
 keenanismic
58
 0-2-10-12-20
 1-14/9-9/8-7/4-14/11
 pentacircle
59
 0-8-10-12-20
 1-16/11-9/8-7/4-14/11
 sensamagic11
60
 0-2-11-12-20
 1-14/9-7/5-7/4-14/11
 utonal
61
 0-7-11-12-20
 1-7/6-7/5-7/4-14/11
 utonal
62
 0-10-11-12-20
 1-9/8-7/5-7/4-14/11
 apollo
63
 0-2-9-13-20
 1-14/9-9/5-12/11-14/11
 octarod
64
 0-8-9-13-20
 1-16/11-20/11-12/11-14/11
 otonal
65
 0-2-11-13-20
 1-14/9-7/5-12/11-14/11
 octarod
66
 0-9-11-13-20
 1-9/5-7/5-12/11-14/11
 octarod
67
 0-2-12-13-20
 1-14/9-7/4-12/11-14/11
 unimarvel
68
 0-8-12-13-20
 1-16/11-7/4-12/11-14/11
 keenanismic
69
 0-11-12-13-20
 1-7/5-7/4-12/11-14/11
 magic
70
 0-7-8-18-20
 1-7/6-16/11-18/11-14/11
 unimarvel
71
 0-7-9-18-20
 1-7/6-9/5-18/11-14/11
 octarod
72
 0-8-9-18-20
 1-16/11-20/11-18/11-14/11
 otonal
73
 0-8-10-18-20
 1-16/11-9/8-18/11-14/11
 pentacircle
74
 0-9-10-18-20
 1-9/5-9/8-18/11-14/11
 apollo
75
 0-7-11-18-20
 1-7/6-7/5-18/11-14/11
 octarod
76
 0-9-11-18-20
 1-9/5-7/5-18/11-14/11
 octarod
77
 0-10-11-18-20
 1-9/8-7/5-18/11-14/11
 magic
78
 0-8-13-18-20
 1-16/11-12/11-18/11-14/11
 otonal
79
 0-9-13-18-20
 1-20/11-12/11-18/11-14/11
 otonal
80
 0-11-13-18-20
 1-7/5-12/11-18/11-14/11
 octarod

Hexads

Number
 Chord
 Transversal
 Type
1
 0-1-2-9-10-11
 1-5/4-14/9-9/5-9/8-7/5
 magic
2
 0-1-2-10-11-12
 1-5/4-14/9-9/8-7/5-7/4
 apollo
3
 0-1-2-9-11-13
 1-5/4-14/9-9/5-7/5-12/11
 magic
4
 0-2-4-9-11-13
 1-14/9-6/5-9/5-7/5-12/11
 octarod
5
 0-1-2-11-12-13
 1-5/4-14/9-7/5-7/4-12/11
 unimarvel
6
 0-2-4-11-12-13
 1-14/9-6/5-7/5-7/4-12/11
 magic
7
 0-2-7-9-11-20
 1-14/9-7/6-9/5-7/5-14/11
 octarod
8
 0-2-9-10-11-20
 1-14/9-9/5-9/8-7/5-14/11
 magic
9
 0-2-7-11-12-20
 1-14/9-7/6-7/5-7/4-14/11
 utonal
10
 0-2-10-11-12-20
 1-14/9-9/8-7/5-7/4-14/11
 apollo
11
 0-2-9-11-13-20
 1-14/9-9/5-7/5-12/11-14/11
 octarod
12
 0-2-11-12-13-20
 1-14/9-7/5-7/4-12/11-14/11
 magic
13
 0-7-8-9-18-20
 1-7/6-16/11-9/5-18/11-14/11
 magic
14
 0-8-9-10-18-20
 1-16/11-9/5-9/8-18/11-14/11
 apollo
15
 0-7-9-11-18-20
 1-7/6-9/5-7/5-18/11-14/11
 octarod
16
 0-9-10-11-18-20
 1-9/5-9/8-7/5-18/11-14/11
 magic
17
 0-8-9-13-18-20
 1-16/11-20/11-12/11-18/11-14/11
 otonal
18
 0-9-11-13-18-20
 1-9/5-7/5-12/11-18/11-14/11
 octarod